The Android Market has some apps which are free software, which entails that anyone can redistribute them; and that are also zero cost. (An example is Theremin, but I'm not interested only in that one specific app.)

So for those apps, there's no good reason for me to register with the Market in order to get those apps and install them. I have no interest in registering with the Market.

It would be good if such free-software and zero-cost apps were available at more places, like the FDroid Repository, which doesn't require anyone's credentials in order to get the apps.

(Please note: this question is not a request for other app stores, that's not the issue.)

But the Android Market doesn't have an obvious way to download apps without logging in. How can I do so?

Google has no way of distinguishing between software that is free but licensed and freeware that has no restrictions (though they could enforce some sort of selection for licence type on upload if they wanted, of course). There is no way (without hacking, presumably) to download apps from the Market without logging in. There's nothing to stop an app maker from providing an alternate download, though.